Simple Question Why Does Pressing P not start the BGE?
Until Blender 2.49, P key put you right into the game engine. 

Blender 2.5 introduced a special concept called Render Engine (Internal, Game, Cycles), and you must choose the right engine to configure it. When you choose the game engine render engine, the properties editor and some other ui menus and panels will update. Pressing P will also now put you in the game engine mode.